{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:53:25Z","timestamp":1777704805479,"version":"3.51.4"},"reference-count":35,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,6,21]]},"abstract":"<jats:p>The rough set theory is an effective method for analyzing data vagueness, while bipolar soft sets can handle data ambiguity and bipolarity in many cases. In this article, we apply Pawlak\u2019s concept of rough sets to the bipolar soft sets and introduce the rough bipolar soft sets by defining a rough approximation of a bipolar soft set in a generalized soft approximation space. We study their structural properties and discuss how the soft binary relation affects the rough approximations of a bipolar soft set. Two sorts of bipolar soft topologies induced by soft binary relation are examined. We additionally discuss some similarity relations between the bipolar soft sets, depending on their roughness. Such bipolar soft sets are very useful in the problems related to decision-making such as supplier selection problem, purchase problem, portfolio selection, site selection problem etc. A methodology has been introduced for this purpose and two algorithms are presented based upon the ongoing notions of foresets and aftersets respectively. These algorithms determine the best\/worst choices by considering rough approximations over two universes i.e. the universe of objects and universe of parameters under a single framework of rough bipolar soft sets.<\/jats:p>","DOI":"10.3233\/jifs-202958","type":"journal-article","created":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T12:15:34Z","timestamp":1617970534000},"page":"11845-11860","source":"Crossref","is-referenced-by-count":7,"title":["Rough approximations of bipolar soft sets by soft relations and their application in decision making"],"prefix":"10.1177","volume":"40","author":[{"given":"Muhammad","family":"Shabir","sequence":"first","affiliation":[{"name":"Department of Mathematics Quaid-i-Azam University, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asad","family":"Mubarak","sequence":"additional","affiliation":[{"name":"Department of Mathematics Quaid-i-Azam University, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Munazza","family":"Naz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Fatima Jinnah Women University Rawalpindi, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"9","key":"10.3233\/JIFS-202958_ref1","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1016\/j.camwa.2008.11.009","article-title":"On some new operations in soft set theory","volume":"57","author":"Ali","year":"2009","journal-title":"Computers and Mathematics with Applications"},{"issue":"4","key":"10.3233\/JIFS-202958_ref2","doi-asserted-by":"crossref","first-page":"3329","DOI":"10.1016\/j.asoc.2011.01.003","article-title":"A note on soft sets, rough soft sets and fuzzy soft sets","volume":"11","author":"Ali","year":"2011","journal-title":"Applied Soft Computing"},{"issue":"13","key":"10.3233\/JIFS-202958_ref3","doi-asserted-by":"crossref","first-page":"4755","DOI":"10.2298\/FIL1813755E","article-title":"Partial soft separation axioms and soft compact spaces","volume":"32","author":"Al-shami","year":"2018","journal-title":"Filomat"},{"key":"10.3233\/JIFS-202958_ref4","doi-asserted-by":"crossref","first-page":"5377","DOI":"10.1007\/s00500-019-04295-7","article-title":"Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone","volume":"24","author":"Al-shami","year":"2020","journal-title":"Soft Computing"},{"issue":"4","key":"10.3233\/JIFS-202958_ref5","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.3906\/mat-2005-117","article-title":"T-soft equality relation","volume":"44","author":"Al-shami","year":"2020","journal-title":"Turkish Journal of Mathematics"},{"key":"10.3233\/JIFS-202958_ref6","doi-asserted-by":"crossref","unstructured":"Al-shami T.M. , Bipolar soft sets: relations between them and ordinary points and their applications, Complexity Article ID 6621854, (2021). https:\/\/doi.org\/10.1155\/2021\/6621854.","DOI":"10.1155\/2021\/6621854"},{"issue":"6","key":"10.3233\/JIFS-202958_ref7","doi-asserted-by":"crossref","first-page":"6537","DOI":"10.3233\/JIFS-182924","article-title":"Some Generalized Operations in Soft Set Theory and Their Role in Similarity and Decision Making","volume":"36","author":"Ayg\u00fcn","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-202958_ref8","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.camwa.2011.05.016","article-title":"Soft topology","volume":"62","author":"\u00c7a\u011fman","year":"2011","journal-title":"Computers and Mathematics with Applications"},{"key":"10.3233\/JIFS-202958_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-020-01161-3"},{"issue":"7","key":"10.3233\/JIFS-202958_ref10","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.2298\/FIL1307183F","article-title":"Soft relations applied to semigroups","volume":"27","author":"Feng","year":"2013","journal-title":"Filomat"},{"issue":"11","key":"10.3233\/JIFS-202958_ref11","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.3390\/math8111891","article-title":"Monad Metrizable Space","volume":"8","author":"G\u00f6\u00e7\u00fcr","year":"2020","journal-title":"Mathematics"},{"issue":"4","key":"10.3233\/JIFS-202958_ref12","doi-asserted-by":"crossref","first-page":"3121","DOI":"10.3934\/math.2021189","article-title":"Amply soft set and its topologies: AS and PAS topologies","volume":"6","author":"G\u00f6\u00e7\u00fcr","year":"2021","journal-title":"AIMS Mathematics"},{"issue":"3","key":"10.3233\/JIFS-202958_ref13","first-page":"23","article-title":"On Soft Topology","volume":"2","author":"Engino\u011flu","year":"2015","journal-title":"El-Cezeri Journal of Science and Engineering"},{"key":"10.3233\/JIFS-202958_ref14","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s12543-012-0104-2","article-title":"Soft Topology","volume":"4","author":"Hazra","year":"2012","journal-title":"Fuzzy Information and Engineering"},{"issue":"2","key":"10.3233\/JIFS-202958_ref15","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s13042-019-00975-w","article-title":"Selectivity analysis of parameters in soft set and its effect on decision-Making","volume":"11","author":"Kamac\u00ed","year":"2020","journal-title":"International Journal of Machine Learning and Cybernetics"},{"issue":"22","key":"10.3233\/JIFS-202958_ref16","doi-asserted-by":"crossref","first-page":"16727","DOI":"10.1007\/s00500-020-04968-8","article-title":"Bipolar N-soft set theory with applications","volume":"24","author":"Kamac\u00ed","year":"2020","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-202958_ref17","first-page":"1","article-title":"Approximation of ideals in semigroups by soft relations","author":"Kanwal","year":"2018","journal-title":"Journal of Intelligent and Fuzzy Systems (Preprint)"},{"key":"10.3233\/JIFS-202958_ref18","unstructured":"Kanwal R.S. and Shabir M. , Approximation of soft set by soft relations, (submitted)."},{"issue":"1","key":"10.3233\/JIFS-202958_ref19","first-page":"105","article-title":"Bipolar Soft Rough Relations","volume":"65","author":"Karaaslan","year":"2016","journal-title":"Communications de la Facult\u00e9,des Sciences de \u013a Universit\u00e9 d\u2019;Ankara. S\u00e9ries A1. Mathematics and Statistic"},{"key":"10.3233\/JIFS-202958_ref20","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1007\/s13370-018-0580-6","article-title":"Bipolar soft rough sets and their applications in decision-making","volume":"29","author":"Karaaslan","year":"2018","journal-title":"Afrika Matematika"},{"issue":"8-9","key":"10.3233\/JIFS-202958_ref21","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/S0898-1221(02)00216-X","article-title":"An application of soft sets in a decision-making problem","volume":"44","author":"Maji","year":"2002","journal-title":"Computers and Mathematics with Applications"},{"issue":"4-5","key":"10.3233\/JIFS-202958_ref22","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/S0898-1221(03)00016-6","article-title":"Soft set theory","volume":"45","author":"Maji","year":"2003","journal-title":"Computers and Mathematics with Applications"},{"issue":"5","key":"10.3233\/JIFS-202958_ref23","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1007\/s00500-017-2883-1","article-title":"Rough fuzzy Rough bipolar soft sets and application in decision-making problems","volume":"23","author":"Malik","year":"2019","journal-title":"Soft Computing"},{"issue":"4-5","key":"10.3233\/JIFS-202958_ref24","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","article-title":"Soft set theory\u2013first results","volume":"37","author":"Molodtsov","year":"1999","journal-title":"Computers and Mathematics with Applications"},{"issue":"4","key":"10.3233\/JIFS-202958_ref25","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.3233\/IFS-130844","article-title":"On fuzzy bipolar soft sets, their algebraic structures and applications","volume":"26","author":"Naz","year":"2014","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"5","key":"10.3233\/JIFS-202958_ref26","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"International Journal of Computer and Information Sciences"},{"key":"10.3233\/JIFS-202958_ref27","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.1016\/j.camwa.2011.02.006","article-title":"On soft topological spaces","volume":"61","author":"Shabir","year":"2011","journal-title":"Computers and Mathematics with Applications"},{"key":"10.3233\/JIFS-202958_ref28","unstructured":"Shabir M. and Naz M. , On bipolar soft sets, (2013). arXiv preprint arXiv:1303.1344."},{"issue":"3","key":"10.3233\/JIFS-202958_ref29","first-page":"359","article-title":"Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces","volume":"39","author":"Shabir","year":"2017","journal-title":"Songklanakarin Journal of Science and Technology"},{"key":"10.3233\/JIFS-202958_ref30","doi-asserted-by":"crossref","first-page":"10801","DOI":"10.1007\/s00500-019-04582-3","article-title":"Reduction of an information system","volume":"24","author":"Shabir","year":"2019","journal-title":"Soft Computing"},{"issue":"3","key":"10.3233\/JIFS-202958_ref31","doi-asserted-by":"crossref","first-page":"4259","DOI":"10.3233\/JIFS-200317","article-title":"Modified rough bipolar soft sets","volume":"39","author":"Shabir","year":"2020","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-202958_ref32","doi-asserted-by":"crossref","unstructured":"Zhang Y. and Yuan X. , Soft Relation and Fuzzy Soft Relation, Fuzzy Information and Engineering and Operations Research and Management, Advances in Intelligent Systems and Computing 211 (2014), Springer, Berlin, Heidelberg.","DOI":"10.1007\/978-3-642-38667-1_21"},{"key":"10.3233\/JIFS-202958_ref33","doi-asserted-by":"crossref","unstructured":"Zhang Z. , Kou X. , Yu W. and Gao Y. , Consistency improvement for fuzzy preference relations with self-confidence: An application in two-sided matching decision-Making, Journal of the Operational Research Society (2020). https:\/\/doi.org\/10.1080\/01605682.2020.1748529","DOI":"10.1080\/01605682.2020.1748529"},{"key":"10.3233\/JIFS-202958_ref34","doi-asserted-by":"crossref","unstructured":"Zhang Z. , Gao Y. and Li Z. , Consensus reaching for social network group decision-making by considering leadership and bounded confidence, Knowledge-Based Systems, 204, (2020). https:\/\/doi.org\/10.1016\/j.knosys.2020.106240","DOI":"10.1016\/j.knosys.2020.106240"},{"key":"10.3233\/JIFS-202958_ref35","doi-asserted-by":"crossref","unstructured":"Zhang Z. , Gao J. , Gao Y. and Yu W. , Two-sided matching decision-making with multi-granular hesitant fuzzy linguistic term sets and incomplete criteria weight information, Expert Systems with Applications (2021), 168. https:\/\/doi.org\/10.1016\/j.eswa.2020.114311","DOI":"10.1016\/j.eswa.2020.114311"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-202958","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:42:03Z","timestamp":1777455723000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-202958"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,21]]},"references-count":35,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.3233\/jifs-202958","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,21]]}}}